Comment: I'm not going to use the anonymous functions because, as far as I know, those are invalid inputs to int and I don't know how int is working with those inputs.
In short: the limits of integration in the two integrals do not cover the same area in the x-y plane.
Because the question states that that second integral is correct, let's start with that
f(x,y) = (112).*exp(-7.*x-9.*y);
I1 = int(int(f(x,y),y,0,x,'hold',true),x,0,sym(1)/sym(4),'hold',true)
I1 is the integral of f(x,y) over the blue triangular area
So, if we want reverse the order of integration then we see that for each value of y, x varies from y to 1/4, and y varies from 0 to 1/4. However, the question shows the limits of integration on y from 0 to 1.
I2 = int(int(f(x,y),x,y,sym(1)/sym(4),'hold',true),y,0,sym(1)/sym(4),'hold',true)